The equation below shows the formula for calculating the shipping cost, C, for book orders, where p is the weight of the books in pounds. There is a $3 handling fee on every order.

Question

C = $0.75p + $3
Which statement is not true about the cost?
The cost for shipping books varies according to the weight of the order.
The cost of the handling fee is unrelated to the weight of the books.
The cost of mailing books increases by $0.75 for each additional pound of books.
The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books.
Done

Answer 1

To analyze the statements, let's break down the formula provided:

C = $0.75p + $3

Where:

• C is the total shipping cost.
• p is the weight of the books in pounds.
• $0.75p is the variable cost based on weight.
• $3 is the fixed handling fee.

Now let's evaluate each statement:

1. The cost for shipping books varies according to the weight of the order.

   • This statement is true. Since the formula includes a variable component ($0.75p) that depends on the weight, the shipping cost will vary as the weight changes.

2. The cost of the handling fee is unrelated to the weight of the books.

   • This statement is true. The handling fee ($3) is a fixed cost that does not change with the weight of the books.

3. The cost of mailing books increases by $0.75 for each additional pound of books.

   • This statement is true. The coefficient of p ($0.75) indicates that for each additional pound, the cost increases by $0.75.

4. The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books.

   • Let's calculate the costs for both 10 pounds and 5 pounds:
     • For 5 pounds: C(5) = $0.75(5) + $3 = $3.75 + $3 = $6.75
     • For 10 pounds: C(10) = $0.75(10) + $3 = $7.50 + $3 = $10.50
     • Twice the cost for 5 pounds would be 2 * $6.75 = $13.50, which is not equal to $10.50.
   • Therefore, this statement is not true.

The statement that is not true is: "The cost of mailing 10 pounds of books is twice the cost for 5 pounds of books."